In this work, several extended approximately invex vector-valued functions of higher order involving a generalized Jacobian are introduced, and some examples are presented to illustrate their existences. The notions of higher-order (weak) quasi-efficiency with respect to a function are proposed for a multi-objective programming. Under the introduced generalization of higher-order approximate in...

We have developed a numerical method based on the transfer matrix to calculate the quasi modes and lasing modes in one-dimensional random systems. Depending on the relative magnitude of the localization length versus the system size, there are two regimes in which the quasi modes are distinct in spatial profile and frequency distribution. In the presence of uniform gain, the lasing modes have o...

In this paper, we study spectral properties of the one dimensional periodic Schrödinger operator with an adiabatic quasi-periodic perturbation. We show that in certain energy regions the perturbation leads to resonance effects related to the ones observed in the problem of two resonating quantum wells. These effects affect both the geometry and the nature of the spectrum. In particular, they ca...

Recently proposed quasi-classical ∂̄-dressing method provides a systematic approach to study the weakly dispersive limit of integrable systems. We apply the quasi-classical ∂̄-dressing method to describe dispersive corrections of any order. We show how calculate the ∂̄ problems at any order for a rather general class of integrable systems, presenting explicit results for the KP hierarchy case. We ...

The synchronous approach to reactive systems, where time evolves by globally synchronized discrete steps, has proven successful for the design of safetycritical embedded systems. Synchronous systems are often distributed over asynchronous architectures for reasons of performance or physical constraints of the application. Such distributions typically require communication and synchronization pr...